Subgroups — C₂×C₃×#376 #84131

Order 384.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²	C₂	1	3	yes	maximal
2	C₃×#376	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₃×#95	C₂	1	4	yes	maximal
4	C₂×#376	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂³×C₃×C₄	C₂²	1	6	yes	—
6	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄²	C₄	1	24	yes	complemented
8	C₂×C₃×C₄²	C₂²	1	12	yes	—
9	C₃×#95	C₂²	1	16	yes	—
10	C₂²×C₄²	C₂×C₃	1	3	yes	—
11	#376	C₂×C₃	1	8	yes	direct product factor
12	C₂×#95	C₂×C₃	1	4	yes	—
13	C₂⁴×C₃	C₂³	1	1	yes	characteristic
14	C₂²×C₃×C₄	—	2	24	no	—
15	C₂²×C₃×C₄	C₂×C₄	1	24	yes	—
16	C₂²×C₃×C₄	C₂×C₄	1	12	yes	—
17	C₂²×C₃×C₄	C₂³	1	12	yes	—
18	C₂²×C₃×C₄	C₂³	1	2	yes	—
19	C₃×C₄²	C₂×C₄	1	48	yes	complemented
20	C₂³×C₄	C₂²×C₃	1	6	yes	—
21	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₄²	C₃×C₄	1	24	yes	complemented
23	C₂×C₄²	C₂²×C₃	1	12	yes	—
24	#95	C₂²×C₃	1	16	yes	—
25	C₂³×C₃	C₂²×C₄	1	6	yes	—
26	C₂³×C₃	#41	1	8	yes	—
27	C₂³×C₃	C₂⁴	1	1	yes	characteristic
28	C₂×C₃×C₄	—	2	48	no	—
29	C₂×C₃×C₄	—	2	24	no	—
30	C₂×C₃×C₄	C₄²	1	16	yes	—
31	C₂×C₃×C₄	C₂²×C₄	1	24	yes	—
32	C₂×C₃×C₄	C₂²×C₄	1	12	yes	—
33	C₂⁴	C₂³×C₃	1	1	yes	characteristic
34	C₂²×C₄	—	2	24	no	—
35	C₂²×C₄	C₂×C₃×C₄	1	24	yes	—
36	C₂²×C₄	C₂×C₃×C₄	1	12	yes	—
37	C₂²×C₄	C₂³×C₃	1	12	yes	—
38	C₂²×C₄	C₂³×C₃	1	2	yes	—
39	C₄²	C₂×C₃×C₄	1	48	yes	complemented
40	C₂²×C₃	C₂×C₄²	1	4	yes	—
41	C₂²×C₃	#117	1	24	yes	—
42	C₂²×C₃	C₂³×C₄	1	3	yes	—
43	C₂²×C₃	C₂×#41	1	4	yes	—
44	C₃×C₄	—	2	24	no	—
45	C₃×C₄	C₂×C₄²	1	8	yes	—
46	C₂³	C₂²×C₃×C₄	1	6	yes	—
47	C₂³	C₃×#41	1	8	yes	—
48	C₂³	C₂⁴×C₃	1	1	yes	characteristic
49	C₂×C₄	—	2	48	no	—
50	C₂×C₄	—	2	24	no	—
51	C₂×C₄	C₃×C₄²	1	16	yes	—
52	C₂×C₄	C₂²×C₃×C₄	1	24	yes	—
53	C₂×C₄	C₂²×C₃×C₄	1	12	yes	—
54	C₂×C₃	#376	1	8	yes	direct product factor
55	C₂×C₃	C₂²×C₄²	1	1	yes	characteristic
56	C₂×C₃	C₂×#117	1	6	yes	—
57	C₂²	C₂×C₃×C₄²	1	4	yes	—
58	C₂²	C₃×#117	1	24	yes	—
59	C₂²	C₂³×C₃×C₄	1	3	yes	—
60	C₂²	C₂×C₃×#41	1	4	yes	—
61	C₄	—	2	24	no	—
62	C₄	C₂×C₃×C₄²	1	8	yes	—
63	C₃	C₂×#376	1	1	yes	characteristic, direct product factor, Sylow
64	C₂	C₃×#376	1	8	yes	direct product factor
65	C₂	C₂²×C₃×C₄²	1	1	yes	characteristic
66	C₂	C₂×C₃×#117	1	6	yes	—

	subgroup	G/H
center	C₂³×C₃×C₄	C₂²
commutator	C₂	C₂²×C₃×C₄²
Frattini, cosocle	C₂³	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃×#376	C₂	direct (N × H)
4. C₂×#376	C₃	direct (N × H)
7. C₂×C₃×C₄²	C₄	semidirect
11. #376	C₂×C₃	direct (N × H)
19. C₃×C₄²	C₂×C₄	semidirect
22. C₂×C₄²	C₃×C₄	semidirect
39. C₄²	C₂×C₃×C₄	semidirect
54. C₂×C₃	#376	direct (N × H)
63. C₃	C₂×#376	direct (N × H)
64. C₂	C₃×#376	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₄²	2
C₃×#376	2
C₂×C₃×#95	2
C₂×#376	3

Subgroups — C2×C3×#376 #84131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#376 #84131